Short- and Long-Range Charge Independence

The difference between the proton-proton (p-p) and neutron-proton (n-p) ¹S₀ interactions attributable to effects of other than electromagnetic origin is discussed in connection with evidence concerning long-range charge independence. The latter evidence is based on the adjustment of the amplitude of the one-pion-exchange (OPE) group of phase parameters to secure best agreement with p-p and n-p scattering data. It is concerned mainly with distant collisions and long-range effects. The ¹S₀ phase shift is appreciably influenced by short-range interactions. Although the pion-mass difference is only ≈3.3%, an appreciably larger fractional difference of effective p-p and n-p ranges, (¹r₀)ₚₚ-(¹r₀)ₙₚ, is shown to be conceivable. In particular, the approximately 10% effect on ¹r₀ obtained by Noyes in his effective-range-type analysis, employing a literal acceptance of the published low-energy n-p data, is not out of the question. The argument used for these conclusions is only semiquantitative. It differs from other earlier treatments in that the reconciliation of short-range charge dependence with long-range charge independence is not made to depend on the adjustment of the shape of the energy curve of the N-N potential versus distance at a distance comparable to the core radius, such as results from an adjustable cutoff radius for the OPE interaction. The adjustments in the shape of the potential-energy curve are those needed to reproduce the phenomenological phase-parameter fits to p-p scattering data, with some direct guidance from the data. The semiquantitative procedure applied to a hard-core potential of the Hamada-Johnston type then yields a fair, though not an exact, reproduction of the phenomenological requirements on the ¹S₀-(n-p) phase shift in the 0-350 MeV incident laboratory energy range. Although the hard-core-potential work makes a 10% difference in the effective ranges conceivable, it favors a smaller effect, such as (¹r₀)ₙₚ=2.7 F. The same procedure, when applied to a soft-core potential somewhat similar to that of Reid, does not give nearly as satisfactory a reproduction of n-p data. It appears possible, though far from certain, that the soft-core potential does not give as satisfactory results because it does not include sufficiently the effect of the smeared out δ function of the OPE potential. The procedure used hybridizes the viewpoints of the S matrix and of the equivalent static nonrelativistic potential, with p-p data fitting playing the role of an analog-computer determination of the parameters of the potential. The speculative character of the frequently made assumption of exact equality of the nonelectromagnetic part of the N-N interaction in $T=1$ states with $L>0$ is emphasized. Evidence regarding the failure of such a view for $L=0$ in the 0-350 MeV energy range is reviewed. The desirability of improving existing experimental information on n-p scattering to the point of making it possible to determine both the $T=1$ and $T=0$ phase parameters for the lower L and J is discussed.